We demonstrate that, in the Chern-Simons and BF theories, the renormalized Schwinger-Dyson functional is related with the generating functional \(Z[J]\)  of the correlation functions of the gauge connections by some kind of duality transformation. Therefore the standard perturbative procedure called “renormalized perturbation theory" [1]} provides a canonical renormalization for \(Z_{SD}[B] \) .
Note that we are not interested in the matrix elements
the composite operator \(\delta S[\phi ] / \delta \phi (x) \) 
between generic states; this issue can be studied by means of standard techniques [1]}, [3]}, [4]}.
Motivated by the results of the topological models with an abelian gauge group, we shall concentrate on the vacuum expectation values of products of operators \(\delta S[\phi ] / \delta \phi (x) \) . In this case, the relationship that we derive between \(Z_{SD}[B] \)  and \(Z[J]\)  shows that the standard technique [1]}, [3]}, [4]} for the study of the renormalization properties of the composite operator \(\delta S[\phi ] / \delta \phi (x) \)  greatly simplifies.
